In both instances? Immediately or hours or days later? I believe he said he contacted his staff the second trip but could not recall when. Do you have information when or if he contacted his staff during the December hospitalization? Not that it really matters, no level of incompetence would ever result in his dismissal.
The authority was transferred prior to Austin's 1st surgery, in Dec.
Hicks would surely be responsible to make sure people in the chain of command would be aware of what was going on, and Austin would be responsible to have tactfully reminded her of that in doing the transfer (plus I'd think there'd be some automatic process kick in the 1st time she issued any directive or command.) -- They probably both deserve a reprimand at least.
In the 2nd instance he says his concern was getting to the hospital, and indeed that sort of problem can be mind-numbingly painful -- I'm kinda inclined to give him a pass on that, and a directive to institute automatic procedures to handle this sort of thing.
I still find the White House not even noticing Austin's absence more troubling.
Now as for you not even watching the vid you are posting...